In this article we reflect on the representation records that intervene in the study of curves and surfaces, as reference mathematical objects, exploring the Sieve-Geometric technique. For this, we analyse the GeoGebra software and the practices of the students of a Master course in Mathematics Education to solve a problem using the paper/pencil environment. The results show that students have mastery of their geometric thoughts in the treatment of objects in the two-dimensional plane, but present difficulties in the representation of geometric objects in three dimensions, which are manifested in the inadequate mobilization of geometric thoughts on the curved and surface sieve, delimiting the geometric object involved in the problem, both in Spatial and Analytical Geometry. [ABSTRACT FROM AUTHOR]